ADDITIVE rho-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES

作者：Park Choonkil^*

来源：Journal of Mathematical Inequalities, 2015, 9(2): 397-407.

DOI：10.7153/jmi-09-33

• Hyers-Ulam stability
• additive rho-functional equation
• additive rho-functional inequality
• non-Archimedean normed space

In this paper, we solve the additive rho-functional inequalities
parallel to f(x+y) - f(x) - f(y)parallel to <= parallel to rho (2f(x +y/2) - f(x) - f(y))parallel to
parallel to 2f(x + y)/2) - f(x) - f(y)parallel to <= parallel to rho (f(x + y) - f(x) - f(y))parallel to,
where rho is a fixed non-Archimedean number with vertical bar rho vertical bar < 1.
Furthermore, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• 出版日期2015-6